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234                               CHEMICAL ENGINEERING
breadth and thickness. It is possible to conceive a fragmental grain having the shape of a long disk with no very sensible thickness which would just pass an aperture in a diagonal position. Grains of this shape regardless of their breadth and thickness will pass the apertures only in the direction of the longest axis. The limit for these grains is as has already been stated that they will just pass the apertures or just refuse to pass . them in the case of square apertures in a diagonal position. In these cases the points of contact or near contact may for practical purposes be considered reduced to two.
Definition of Perfect Grading Device According to Diameter.—It is perfectly evident that one element of screens is positive or rigid, that is the apertures of any two screens which take part in a grading rigidly limits the over and under size. On the other hand, the trial for different axial positions is haphazard. Grains which will pass the apertures in -only one or a few positions seldom get' this opportunity. Pines and pieces markedly smaller than the apertures of the pair of screens with the smallest opening will be readily eliminated but not the .pieces near the size of these openings. In good commercial grading a screen size will appear to consist almost entirely of grains of the size of the apertures in the screen with the smaller holes of the pair taking part in the grading.
In all cases of commercial grading the eye is in the end the sole and final criterion of grading. If the pieces comprising the grading appear to be all of a size the work is regarded as sufficiently good. The use of hand screens to test the work of power screens does little more than satisfy the eye as must be evident upon reflection. As will be shown later perfect work cannot be done by any motion imparted to a screen either by hand or power although the more prolonged the screening movements the nearer perfection and the former should be the better. Power screens are all more or less deficient in providing the complicated movements necessary for approaching nearly perfect grading. In most power-driven machines the means for progressing the material are the most important. In others where some attempt is made to duplicate the complexity of movement to be obtained by hand screening the imitation is not carried far enough or near enough to the hand movements to obtain much useful result. All such complexity also often adds to the wear and tear of the screen and the actuating mechanism. Where tonnage is the desideratum rather than perfection of screening the simplest possible progressive means usually provides for screening means which are sufficiently good provided the screening device is not overloaded.
In the most precise commercial grading, the best work being done in the abrasive industry, the efficiency of the work does not run much over 75 per cent. As shown by hand-screen testing the work is better than this, in some cases over 90 per cent. In making this statement about efficiency perfect work is the criterion and not the usual test work done by hand screens.
A perfect grading device according to diameter would be one which rigidly limits the size as screens do and which gives each grain a trial at the apertures in a multitude of axial presentations so as to make sure that every grain which can possibly go through the apertures does so. There is of course no screening device on the market which provides this positive action but other things being equal the nearer the screening device approaches this Ultima Thule the better it is.
Shape of Fragments.—Most material on being comminuted by crushing or shredding usually breaks up into fragments which have the same general shape in all the sizes. In the case of rock and ore crushing or other hard and resistant material the fragments are more angular in the coarser sizes and more rounded in the finer sizes. Where material breaks into fragments which to the casual